The　combination　of　artificial　intelligence　and　finite　element　method　(FEM)　is　a　hot　topic　in　the　field　of　computational　mechanics.　This　study　proposes　a　novel　base　force　element　method　(BFEM)　for　finite　strain　problems　based　on　the　complementary　energy　principle.　Using　the　back-propagation　(BP)　neural　network　in　the　field　of　artificial　intelligence　to　construct　the　constitutive　relationship　of　the　BFEM　for　finite　strain　problems.　First,　a　BFEM　model　for　finite　strain　problems　was　derived.　Second,　using　the　BP　neural　network　model　and　learning　from　test　samples,　a　constitutive　relationship　for　incompressible　finite　strain　problems　has　been　efficiently　established.　Third,　the　program　has　been　upgraded　using　parallel　computing　and　sparse　matrices,　which　greatly　improves　the　computational　efficiency　of　this　study.　Finally,　several　finite　strain　examples　were　used　to　verify　the　correctness　of　the　BFEM　based　on　the　BP　neural　network　proposed　in　this　study,　as　well　as　the　efficiency　of　the　parallel　computing　method.　This　study　combines　BP　neural　network　with　a　new　type　of　FEM　—　BFEM,　which　fills　the　gap　in　using　complementary　energy　FEM　to　calculate　the　finite　strain　problem　of　incompressible　hyperelastic　materials.　©　World　Scientific　Publishing　Company.